{"id":4627,"date":"2024-10-24T10:15:27","date_gmt":"2024-10-24T06:15:27","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=4627"},"modified":"2026-04-19T17:28:47","modified_gmt":"2026-04-19T13:28:47","slug":"valuation-of-real-options","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/","title":{"rendered":"<span class=\"eon-recovered-georgian-title\" data-no-translation=\"\">\u10e0\u10d4\u10d0\u10da\u10e3\u10e0\u10d8 \u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10d8\u10e1 \u10e8\u10d4\u10e4\u10d0\u10e1\u10d4\u10d1\u10d0<\/span>"},"content":{"rendered":"<p class=\"wp-block-paragraph\">The valuation of real options can be approached in the same way as financial options, though the main issue here is finding the correct discount rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To remind you, real options involve decisions that are irreversible or nearly irreversible, such as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The option to delay starting a project (Call);<\/li>\n\n\n\n<li>The option to expand production (Call);<\/li>\n\n\n\n<li>The option to &#8220;stretch&#8221; production over time (Call);<\/li>\n\n\n\n<li>The option to abandon a project (Put);<\/li>\n\n\n\n<li>The option to reduce production (Put).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">What\u2019s interesting here:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A decision tree of events and choices is used to understand and evaluate real options. This diagram helps illustrate what decisions are rational under different scenarios and what the expected outcome is. However, the challenge lies in finding the appropriate discount rate for the resulting outcomes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To make this clearer, let\u2019s look at a specific example from the book*:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"656\" data-attachment-id=\"4638\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-192\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-21.png?fit=1145%2C656&amp;ssl=1\" data-orig-size=\"1145,656\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-21.png?fit=1024%2C587&amp;ssl=1\" class=\"wp-image-4638\" style=\"width: 1000px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-21.png?resize=1145%2C656&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It\u2019s about a project for producing innovative fuel, evaluated from three different perspectives:<br \/>A &#8211; Winning a government tender,<br \/>B &#8211; Selling to car manufacturers, and<br \/>C &#8211; Waiting, observing the market, and selling directly to consumers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Three types of risks are presented:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Technical (Will it even work? &#8211; beta = 0)<\/li>\n\n\n\n<li>Competitive (Will we win the tender? &#8211; beta = 0)<\/li>\n\n\n\n<li>Market (What will oil prices be like? &#8211; Beta > 0)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">I will briefly discuss each project to touch on finding the discount rate, and later, I will upload an Excel model for those interested in the details:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Project A &#8211; Government Tender<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s the situation: the organization must invest today to start working on innovative fuel production. The government tender will be held in a year, and they will either win it or not.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If the project succeeds, additional investment will be needed, and there will be profit, though we can decline the project. If we don\u2019t win, there\u2019s still an option to make additional investments and sell the results as a patent.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the tender\u2019s outcome isn\u2019t related to market risks, we assume Beta = 0, meaning discounting at the risk-free rate isn\u2019t a problem. In this example, the risk-free rate is 0%. The numbers and diagram are as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"403\" height=\"301\" data-attachment-id=\"4649\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-193\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-22.png?fit=403%2C301&amp;ssl=1\" data-orig-size=\"403,301\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-22.png?fit=403%2C301&amp;ssl=1\" class=\"wp-image-4649\" style=\"width: 400px\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-22.png?resize=403%2C301&#038;ssl=1\" alt=\"\"\/><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-40.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"715\" height=\"477\" data-attachment-id=\"4810\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-215\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-40.png?fit=715%2C477&amp;ssl=1\" data-orig-size=\"715,477\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-40.png?fit=715%2C477&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-40.png?resize=715%2C477&#038;ssl=1\" alt=\"\" class=\"wp-image-4810\" style=\"width:400px;height:auto\"\/><\/a><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Project B &#8211; Wholesale Sales<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The investment parameters change. Here, the project involves producing a different type of fuel, and the results after one year depend on what the oil prices will be. If oil prices are favorable, we have the option to make additional investments and achieve good results, but if prices are bad, we can avoid further investments and simply sell the project.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-24.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1122\" height=\"489\" data-attachment-id=\"4655\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-195\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-24.png?fit=1122%2C489&amp;ssl=1\" data-orig-size=\"1122,489\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-24.png?fit=1024%2C446&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-24.png?resize=1122%2C489&#038;ssl=1\" alt=\"\" class=\"wp-image-4655\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The question is: what discount factor should we apply to the resulting $500M?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If we discount it at the risk-free rate and subtract today\u2019s investment, we get $400M, which is incorrect, as oil prices are tied to their beta, on which the project depends.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The example doesn\u2019t provide oil price beta. However, it gives today\u2019s option prices on oil and their returns, which allow us to deduce the discount rate for this option, which turns out to be 100%. Based on this, discounting the project\u2019s NPV gives $150M, which is also incorrect since the risk of the option and its underlying asset are not the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The good news is that with the given option data, we can create a hypothetical portfolio. By combining these \u201coptions\u201d and \u201cloans,\u201d we can create a portfolio that replicates the same results as the project.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The value of this replicating portfolio will be exactly the same as the project\u2019s PV:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-25.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"443\" height=\"468\" data-attachment-id=\"4663\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-196\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-25.png?fit=443%2C468&amp;ssl=1\" data-orig-size=\"443,468\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-25.png?fit=443%2C468&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-25.png?resize=443%2C468&#038;ssl=1\" alt=\"\" class=\"wp-image-4663\"\/><\/a><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Project C &#8211; Waiting<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Project C adds a waiting option. The question is whether to invest today or wait and invest in a year.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-26.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"735\" height=\"559\" data-attachment-id=\"4666\" data-permalink=\"https:\/\/eoninvestment.com\/ka\/2024\/10\/24\/valuation-of-real-options\/image-197\/\" data-orig-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-26.png?fit=735%2C559&amp;ssl=1\" data-orig-size=\"735,559\" data-comments-opened=\"1\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-26.png?fit=735%2C559&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/image-26.png?resize=735%2C559&#038;ssl=1\" alt=\"\" class=\"wp-image-4666\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">I won\u2019t go into the details of this example, but it\u2019s available in the Excel file, and I will highlight key points:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The example gives oil price beta (0 or 1), and the discount rate is derived from the CAPM. This is how the top branch is calculated (we could have done the same in Project B).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The lower branch is the waiting option, and we cannot directly apply oil price beta to it, so here too, a replicating portfolio of the \u201cupper branch\u201d and a \u201cloan\u201d needs to be created.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The example also illustrates the use of a risk-free world assumption method, which yields exactly the same results as the portfolio replication method.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/eoninvestment.com\/wp-content\/uploads\/2024\/10\/21.-fuelco.xlsx\">Valuation of Real Options &#8211; Excel<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>P.S.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These are quite intricate examples, so if you&#8217;re interested in the details, it&#8217;s better to refer to the source. The Excel file will be useful if the Plan Tree is added in Excel.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Source: Venture Capital &#038; the Finance of Innovation &#8211; by A. Metrick<\/p>","protected":false},"excerpt":{"rendered":"<p>\u10e0\u10d4\u10d0\u10da\u10e3\u10e0\u10d8 \u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10d8\u10e1 \u10e8\u10d4\u10e4\u10d0\u10e1\u10d4\u10d1\u10d0 \u10e8\u10d4\u10e1\u10d0\u10eb\u10da\u10d4\u10d1\u10d4\u10da\u10d8\u10d0 \u10d8\u10e1\u10d4\u10d5\u10d4 \u10e0\u10dd\u10d2\u10dd\u10e0\u10ea \u10e4\u10d8\u10dc\u10d0\u10dc\u10e1\u10e3\u10e0\u10d8 \u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10d8\u10e1, \u10d7\u10e3\u10db\u10ea\u10d0 \u10d0\u10e5 \u10db\u10d7\u10d0\u10d5\u10d0\u10e0\u10d8 \u10e1\u10d0\u10d9\u10d8\u10d7\u10ee\u10d8 \u10e1\u10ec\u10dd\u10e0\u10d8 \u10d3\u10d8\u10e1\u10d9\u10dd\u10dc\u10e2\u10d8\u10e0\u10d4\u10d1\u10d8\u10e1 \u10d2\u10d0\u10dc\u10d0\u10d9\u10d5\u10d4\u10d7\u10d8\u10e1 \u10db\u10d8\u10d2\u10dc\u10d4\u10d1\u10d0\u10d0. \u10d2\u10d0\u10d2\u10d0\u10ee\u10e1\u10d4\u10dc\u10d4\u10d1\u10d7, \u10e0\u10dd\u10db \u10e0\u10d4\u10d0\u10da\u10e3\u10e0 \u10dd\u10e4\u10ea\u10d8\u10d4\u10d1\u10e8\u10d8 \u10db\u10dd\u10d8\u10d0\u10d6\u10e0\u10d4\u10d1\u10d0 \u10d8\u10e1\u10d4\u10d7\u10d8 \u10d2\u10d0\u10d3\u10d0\u10ec\u10e7\u10d5\u10d4\u10e2\u10d8\u10da\u10d4\u10d1\u10d4\u10d1\u10d8 \u10e0\u10dd\u10db\u10d4\u10da\u10d7\u10d0 \u10e8\u10d4\u10db\u10dd\u10d1\u10e0\u10e3\u10dc\u10d4\u10d1\u10d0 \u10e8\u10d4\u10e3\u10eb\u10da\u10d4\u10d1\u10d4\u10da\u10d8 \u10d0\u10dc \u10d7\u10d8\u10d7\u10e5\u10db\u10d8\u10e1 \u10e8\u10d4\u10e3\u10eb\u10da\u10d4\u10d1\u10d4\u10da\u10d8\u10d0, \u10db\u10d0\u10d2\u10d0\u10da\u10d8\u10d7\u10d0\u10d3: \u10de\u10e0\u10dd\u10d4\u10e5\u10e2\u10d8\u10e1 \u10d3\u10d0\u10ec\u10e7\u10d4\u10d1\u10d8\u10e1 [\u2026]<\/p>","protected":false},"author":12998525,"featured_media":4666,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_eon_insights_quality":"","_eon_insights_decision":"","_eon_insights_destination":"","_eon_insights_merge_group":"","_eon_insights_required_changes":"","_eon_insights_start_order":0,"_eon_featured_insight":0,"_eon_insights_map_version":"","_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[31110612,774675955,106538530,164077271],"tags":[178,179,4269,6635,8589],"eon_topic":[],"eon_learning_path":[],"eon_collection":[],"eon_level":[784445728],"eon_content_type":[],"eon_source":[784445711],"eon_idea":[784445705,784445697],"eon_framework":[],"class_list":["post-4627","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-excel-models","category-venture-capital-the-finance-of-innovation-by-a-metrick-a-yasuda","category-derivatives","category-vc-valuation","tag-books","tag-business","tag-finance","tag-investing","tag-stocks","eon_level-advanced","eon_source-venture-capital-the-finance-of-innovation-by-a-metrick-a-yasuda","eon_idea-derivatives","eon_idea-vc-valuation"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - 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